Talk:Great Pyramid of Giza

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Answer to "52 degrees" question
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"Additionally, it has been alleged (notably by the "sleeping prophet" Edgar Cayce?) that the dimensions and details of the great pyramid, properly interpreted, provide prophecies of events in modern times."

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No, Cayce said a lot of ... questionable things, but I think the "dimensions giving prophecy" schtick was somebody else's. I'll look and let you know. Some Italian guy .... not Schiaparelli. More later.

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- Here

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http://www.skeptics.com.au/journal/paramyth.htm

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Invented by John Taylor, elaborated by Charles Piazzi Smyth, Astronomer Royal for Scotland (my "Italian guy" - don't know what his ethnicity was really.)

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----

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Yeah, I may be misremembering that, but I'm pretty sure he at least commented on it (but then he commented on just about every other bit of psychic nonsense of his time). --LDC

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I see Cayce "readings" on the Web that mention the idea, but it's difficult to pin down Cayce's language as to what he's really trying to say.

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-- Here

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http://www.nhne.com/specialreports/srpyramid.html

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a "reading" about a secret hall of records of *ancient* events, not specifying whether this includes prophecies or not.

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LOL - http://www.margaretmorrisbooks.com/xcerpt08.html

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- the following "shows that some of the claims associated with this idea are too strange to take seriously".

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We should have something in the page about the astronomical alignments, also.

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Kate Spence has a theory on astronomical alignments. Unfortunately her Nature article of 11 Nov 2000 seems unavailable, but a google search of "Kate Spence" reveals a cached page with the article; look for header "Feature of the week > Pyramid precision".

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:I have a copy of the paper. Spence figures several pyramid baselines were set in

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:How long it took to finish them is another question. Also, it's been several years; I don't know what the current thinking about Spence's work is.

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:--[[User:Wwoods|wwoods]] 00:29, 23 May 2004 (UTC)

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The statement that the pyramid has moved 4 kilometers South could also mean its original alignment has also shifted. Is there a reference concerning the 4 kilometer shift?

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'''Date of completion:''' I've just changed 2680 to 2570. 2680 is about 100 years too early, particularly in light of the dates given for [[Khufu (pharaoh)|Khufu]]'s reign in his article. 2570 would place completion in the final years of K's stint in the top spot.

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So, what are the dimensions of the pyramid? The imperial and metric measurements don't exactly agree with each other (only accurate to 2 s.f.).

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Also, where does 52 degrees come from? If we take ''h'' as 146m and ''s'' as 235m, my calculations show that it is approximately 41 degrees:

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<math>\tan^{-1} \left( \frac{\frac{h}{\sin \left( 45^\circ \right) }}{s} \right) \approx 41.303^\circ</math>

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-[[User:Zhen Lin|Zhen Lin]] 16:23, 14 Apr 2004 (UTC)

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:A cross-section of the pyramid containing the peak and parallel to opposite sides of the base will be a triangle of height 146.5 m and base 230.5 m. Therefore, the slope of the sides of the pyramid is

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:<math>\tan^{-1}\left({146.5\over230.5/2}\right)\approx51.81^\circ.</math>

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:—[[User:Bkell|Bkell]] 04:32, 13 Jun 2005 (UTC)

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== References? ==

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I'd be interested to see some references for the following statements in the article:

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# The chamber which is most normal in its situation is the subterranean chamber; but this is quite unfinished, hardly more than begun.

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# ...there is very credible testimony to a sarcophagus having existed in the queen's chamber, as well as in the king's chamber.

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# It was previously believed that slaves were used as labor, but that view is now rejected by almost all modern-day scholars.

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For (1), it's unclear to me what "normal" standard of reference is being used. Other pyramids? And by "unfinished", are we assuming that the chambers within the pyramid were intended for use as tombs? (I find it somewhat unlikely that anyone would go to all the trouble to build the Great Pyramid and then not bother "finishing" the inside.) For (2), what is the "very credible testimony"? And for (3), some more explanation about who, in particular, devised and supported the slave-labor theory, and maybe the names of a couple of the "almost all" scholars who have since rejected that theory. I'll see if I can't find some references for these myself, in the meantime... -- [[User:Wapcaplet|Wapcaplet]] 21:48, 22 May 2004 (UTC)

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:'''Unfinished Chamber'''

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:This unfinished subterranean chamber, an unfinished chamber within Khufu's Pyramid, lies 90 feet (30 meters) below the surface of the plateau, and is closed to the public. Standing alone inside this oxygen-deficient space is quite an experience; 2.3 million blocks of stone weighing some 6.5 million tons loom overhead. Workers down here chipped away at the limestone bedrock to build what is thought to be the original burial chamber for King Khufu. Egyptologists believe the chamber is 'unfinished' because Khufu suddenly decided he wanted his burial chamber to be higher in the pyramid, and ordered the workers to stop. Khafre's Pyramid follows a similar pattern, with an unfinished subterranean burial chamber.

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:http://www.pbs.org/wgbh/nova/pyramid/explore/khufuunflo.html

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:'''Queen's Chamber'''

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:Although it is called the 'Queen's Chamber,' Egyptologists believe this space was meant to be the final resting place for King Khufu, until he changed his mind yet again and opted for a burial chamber even higher. The roof of the chamber is raised at its center.

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:http://www.pbs.org/wgbh/nova/pyramid/explore/khufuqueenhi.html

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:--[[User:Wwoods|wwoods]] 00:29, 23 May 2004 (UTC)

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Those are good, though almost as vaguely worded as what we already have. I did find a fairly thorough source on construction, labor force, orientation, etc. [http://www.touregypt.net/featurestories/pyramids.htm here] (skip past the lame touristy introduction to the links at the bottom), including some great [http://www.touregypt.net/featurestories/pyramidlifts.htm illustrations] about how possible ramp configurations used to get blocks up the side. Lots of references to the specific people who came up with various theories. I think I'll build on those when I find some time.

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Also, I've been thinking about that claim to a [[pi]] ratio. It all boils down to the exact angle of the slope; if my math is correct, a slope of 51°51'14.306" would yield pi accurate to six decimal places. Most of the measurements I've seen indicate that the slope is closer to 51°50'40", giving pi accurate to 2 decimal places (3.142668...), closer to 22/7 than pi. I've seen varying estimates of the slope, though; less than 1 minute of error makes all the difference. -- [[User:Wapcaplet|Wapcaplet]] 04:41, 23 May 2004 (UTC)

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== New image addition ==

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The recently-added image [[:Image:Pyramids of Egypt.jpg]] does not appear to resemble anything now standing on the Giza plateau. Unless the illustration really is of the Giza pyramids, particularly the Great Pyramid (albeit a quite liberal interpretation), I don't think it belongs on the article. -- [[User:Wapcaplet|Wapcaplet]] 19:16, 24 Nov 2004 (UTC)

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* After looking around a bit, it appears that this image is by 16th-C. Dutch artist [[Martin van Heemskerck|Maerten van Heemskerck]]. [http://encarta.msn.com/media_461538596/engraving_of_Pyramids_of_Egypt.html] Judging by the resemblance, I'd say he must have done the engraving based on verbal description alone. I still don't think it belongs here. Maybe on [[Seven Wonders of the World]], since it needs an image. -- [[User:Wapcaplet|Wapcaplet]] 19:29, 24 Nov 2004 (UTC)

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:: I agree, and said as much on [[Image talk:Pyramids of Egypt.jpg|its talk page]]. If no one objects by the end of the week I'm going to change the image text or delete it entirely. I don't care if I orphan it. If it's near and dear to someone's heart you'd better come to its rescue. — [[User:Clarknova|Clarknova]] 03:25, 1 Dec 2004 (UTC)

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==Close-up picture==

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That's Khafre, not Khufu.

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* So it is. And someone also removed the "right" indicator in the caption to the other image showing all three. I've fixed to clarify (kept the image, though). -- [[User:Wapcaplet|Wapcaplet]] 19:32, 3 Feb 2005 (UTC)

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==NPOV==

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This article is beginning to need a neutrality overhaul. I [http://en.wikipedia.org/w/index.php?title=Great_Pyramid_of_Giza&diff=9935831&oldid=9918351 started], but there's much left to do. For instance:

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* "''As has been proven by papyrus documents, each side measured in Antiquity 440 Old Royal Cubits (230.5 m).''" -- Reference is needed. What papyrus documents?

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::''For the reference:''   Look to this [http://www.fig.net/pub/athens/papers/wshs2/WSHS2_1_Lelgemann.pdf document] ''(section 2.1)'' of the Director of the Berlin Geodesic Institute: He mentions in his article Mr. Petrie who found this papyrus document in 1934.

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:: -- [[User:Paul Martin|Paul Martin]] 22:42, 28 Feb 2005 (UTC)

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::P.S. ''The metrologist Livio C. Stecchini wrote:'' "It is agreed amount serious scholars that the side was calculated as 440 Egyptian royal cubits."

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* "''The grand gallery also contained some sort of mechanism for the release of a huge stone block which plugged the ascending passage.''" -- I don't doubt that this is true, but some evidence for and better description of such a mechanism would be useful.

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* "''The entire upper part of the pyramid was thus sealed after the burial of the king.''" -- Again, how do we know this? As far as I know, no evidence exists that a king was even buried here. We need references one way or another. There are other references throughout to "burial chamber of the king", "king's burial chamber", etc. which should probably be rendered as simply "King's chamber," given the dispute over whether a king was actually buried here.

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* An oddity about the "graffiti" on the relieving stones in the King's chamber: that it is "''the only evidence which proves that pharaoh Hor Medjedu Khnum Khufu had the Great Pyramid built.''" If this is the ''only'' evidence, then it's hardly proof of the pyramid's builder; this matter is under dispute, and maintaining neutrality requires that we try to avoid such unilateral statements.

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* In the section detailing various estimates of the labor force required, the section "''Nevertheless, given the subsequent absurd implications of these theories ... they fall terribly short of providing a satisfactory explanation''" is in serious need of rephrasing. Whether a theory is absurd or satisfactory is rather subjective; put the notion of absurdity in context, and make note of who finds the various theories absurd or satisfactory (or, better, simply note some of the theories, are those who dispute them, and let readers make their own judgments).

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* The article is arguing with itself. "''Second, if huge quantities of earth were dug and moved to support the ramps instead, geological indications would undoubtedly reveal this today. (Present day studies do yield such a revelation! But the ramp size uncovered is too small. See external links below.)''" This is bad. It gets even more ridiculous in the sentences that follow.

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* "''Some sort of ancient Steam engine is undeniably and absolutely required for a reasonable time period within which to carefully construct such a monument of this size.''" This is qualified in previous sentences, but it still comes across as being a statement of fact, especially with the excessive emphasis used.

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* Finally, the image at the very bottom showing "RJ or RL-shaped supports" needs some kind of reference. I couldn't find anything about these supports via Google.

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The total effect of the above is to make the article seem non-credible. Let's see if we can clean it up. -- [[User:Wapcaplet|Wapcaplet]] 20:48, 6 Feb 2005 (UTC)

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OK, in a second crack at culling the POV, I've removed some things. First, this paragraph:

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<blockquote>Nevertheless, modern estimates for ancient Egyptian population size around the time that the pyramid was constructed fail at lending substantial credence for these assertions. (See http://www.etext.org/Politics/World.Systems/papers/modelski/geocit.htm .) And there are other serious technical questions posed as well, discussed as follows.</blockquote>

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The article referenced makes little mention of Giza, and none whatever regarding the population estimate being in conflict with various labor force size estimates for the Great Pyramid. I have also removed:

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<blockquote>Nevertheless, given the subsequent absurd implications of these theories -- ... in 2600 BC ... covering an area of seven city blocks and weighing six and a half million tons ... in less than thirty years, the workers had to raise over two million blocks to a height of forty stories at the rate of one block every three minutes ... [using] only the simplest technology (http://www.pbs.org/wgbh/nova/transcripts/1915mpyramid.html) -- they fall terribly short of providing a satisfactory explanation.</blockquote>

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Indeed, ''this article'' does not provide a very convincing explanation of how this may have been accomplished, and this is one area that could use some work. However, this part of the article is merely noting some of the estimates that have been made regarding the labor force needed. It's not our job (as authors of this article) to point out flaws in the reasoning of those who did the estimates. If you need to point out flaws, please find another publication that does it for you, and reference it.

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The next removal:

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<blockquote>Though this "ramp theory" is the popular perception today, it is not without some serious fundamental problems. First, there remains considerable debate over exactly what kinds of ramps might have been used, because various ramp designs implicate technological advances that the ancient Egyptians clearly did not have. (See [[Civil engineering]].) Second, if huge quantities of earth were dug and moved to support the ramps instead, [[Geology|geological]] indications would undoubtedly reveal this today. (Present day studies ''do'' yield such a revelation! But the ramp size uncovered is too small. See external links below.) Third, given even adequate resolutions to these first two problems, the most serious fundamental problem still remaining is that of ''time.'' Even if we were to multiply the given time period above (i.e., 30 years) many, many times over, we would still fail once again at reaching a workable conclusion. Only by lengthening the given time period to ''several millennia (!)'' may we arrive at an adequate time frame with which to cut (''with [[chisel]]s?''), transport (''[[mile]]s!''), lift (''human muscle?''), maneuver (''with [[wood|board]]s and [[rope]]?'') and fit (''smoothing/reshaping some'') each of the over two million stone blocks! ''Note that some of the stone blocks weigh several [[ton]]s!!''</blockquote>

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It was much easier to remove this paragraph than to edit out all the exclamation points (both literal and metaphorical). This was cut for the same reasons as above. Articles shouldn't make unsupported assertions (that is, assertions backed up only by patchwork arguments, rather than by references). Ditto for the following:

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<blockquote>Modern day [[Historical revisionism|Revisionists]] speculate that there could be only one logical conclusion to explain all the above. (See also [[Origins of chess|origins of chess]] and [[Silk Road]]'': '''Origins,''' bottom paragraph,'' for an adequate understanding.) The only way possible that the ancient Egyptian laborers could have accomplished this monumental feat in anything resembling a reasonable amount of time is with [[chain]]s/[[cable]] and some sort of [[Crane (machine)|Ancient crane]]. The conclusion may run contrary to popular perception, but the facts point only in this direction. Some sort of ancient [[Steam engine]] is ''undeniably'' and ''absolutely'' required for a reasonable time period within which to carefully construct such a monument of this size. ''See external links and image below.''</blockquote>

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The end result is that this section of the article is more or less as it was at the beginning of November 2004. I don't deny that this section is in need of much work, but the above paragraphs do more harm than good, in my estimation. If anyone is interested in restoring these paragraphs, please back them up with references: facts, publications, and who, especially, has made these assertions. -- [[User:Wapcaplet|Wapcaplet]] 04:45, 7 Feb 2005 (UTC)

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== Rushing to Defend an Erroneous Deletion ==

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Dear Mr [[User:Wapcaplet|Wapcaplet]]:

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We understand your point of view. History says one thing, but rational logic says another. [[Historical revisionism]] always begins this way.

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History is repeating itself, because this same sort of affair happened in March of 2004 at [[Origins of chess]] when we first proposed an ancient Egyptian origin to the game. Needless to say, the proposal was blasted off the web page and moved to "Talk." Nevertheless, we sat quietly and watched as everyone pondered it over ... and what do you know? Have you read [[Origins of chess]] lately? There's even a photograph of the [[Sphinx]] and the [[Great Pyramid of Giza]] at the very top of that web page now!

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So, here we go again .... :)

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The following discussion is rooted in web links that I've been able to find on the Internet.

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'''NUMBER 1:''' To respond to your earnest request,

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::If anyone is interested in restoring these paragraphs, please back them up with references: facts, publications, and who, especially, has made these assertions,

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let's start by quoting ''... '''Wikipedia!!!''' ''

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::'''[[Scientific method]]:''' Our earliest records of ''anyone'' (much less a scientist) adhering to this strict process comes from ancient Egypt.

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You see. The ancient Egyptians were using the scientific method ''millennia'' before [[Francis Bacon]] even knew how to write. And see here: [[Bridge]]''': History''' and [[Cement]]. We could pile one astounding advance on top another. Take a look at the pyramids: Millions of stone blocks ... some weighing several tons.

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[[Ancient history]] proceeds in probabilities. The ancient Egyptians knew the scientific method ''millennia'' before anyone else did. What are the implications? Francis Bacon lived and died only a few hundred years ago. [[Isaac Newton]], around the same time. English history records only a short span of time (relatively speaking) between scientific processes and mathematical advancement.

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Here are some others you'd likely find interesting:

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::[[Demographics of Egypt]]: Archeological findings show that primitive tribes lived along the Nile long before the dynastic history of the pharaohs began. By 6000 B.C., organized agriculture had appeared.

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::[[Figurine]]: Read the bit on [[Morocco]].

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'''NUMBER 2: [[Moscow and Rhind Mathematical Papyri]]'''

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::In summary, we cannot prove that the ancient Egyptians knew calculus. We can say however that the evidence suggests so.

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::In addition to these two historical texts, there is other evidence demonstrating an ancient Egyptian knowledge of basic mathematics and even [[surveying]] as early as [[3000 BC]]. [http://ag.arizona.edu/ABE/People/Faculty_Homepages/Cuellos_Homepage/Thoughts/ibe7.htm [1]] See also [[Timeline of mathematics]].

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::Besides describing how to obtain an approximation of <math>\pi</math> accurate to within less than one per cent, it also describes one of the earliest attempts at [[squaring the circle]] and in the process provides persuasive evidence against the theory that the Egyptians deliberately built their [[pyramid]]s to enshrine the value of <math>\pi</math> in the proportions. Even though it would be a strong overstatement to suggest that the papyrus represents even rudimentary attempts at analytical geometry, Ahmes did make use of a kind of an analogue of the [[cotangent]]. Furthermore, quoting ''Mathpages.com,''

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::::... the 2/n table of the Rhind Papyrus, which dates from more than a thousand years before Pythagoras, seems to show an awareness of prime and composite numbers, a crude version of the 'Sieve of Eratosthenes,' a knowledge of the arithmetic, geometric, and harmonic means, and of the 'perfectness' of the number 6. This all seems to suggest a greater number-theoretic sophistication than is generally credited to the ancient Egyptians. ([http://mathpages.com/home/rhind.htm ''The Rhind Papyrus 2/N Table''])

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'''NUMBER 3: Population Size'''

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::Many varied estimates have been made regarding the labor force needed to construct the Great Pyramid. Herodotus, the Greek historian in the 5th century BC, estimated that construction may have required the labor of 100,000 slaves for 30 years. Polish architect Wieslaw Kozinski believed that it took as many as 25 men to transport a 1.5-ton stone block; based on this, he estimated the workforce to be 300,000 men on the construction site, with an additional 60,000 off-site.

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The key number here is 300,000, because it has been argued that the ancient Egyptians ''could have supplemented their work force'' with slaves. Here are a couple references you'd likely be interested in:

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::[http://timelines.ws/0B3300_1300BC.HTML ''Timeline 3300 to 1300 BCE'']: ''ca 2800BCE - Khufu commanded the building of the Great Pyramid. It took an estimated 100,000 people 30 years to construct.'' (WH, 1994, p.12)(K.I.-365D, p.122)(HT, 5/97, p.26)

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::[http://lexicorient.com/cgi-bin/eo-direct-frame.pl?http://i-cias.com/e.o/egypt_a.htm ''Encyclopaedia of the Orient'']: ''The main urban places of Egypt through the main part of the history of Ancient Egypt, were Memphis and Thebes.''

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To pause before continuing,

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*100,000 is too small a number. Herodotus, who lived in the 5th century BC, didn't know what he was talking about. Kozinski calculated a better number, but his number is too big, as evidenced by Professor Modelski's paper.

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*Even if you don't consider Memphis' proximity to the Great Pyramid of Giza significant, you must yield to its prominent status in ancient Egyptian history as ''capital'' and ''main urban place.''

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Nevertheless, as pointed out, population size is '''NOT''' ''the most serious fundamental problem.'' This is an important point, as said before [[Ancient history]] proceeds in probabilities. We may spend an entire day arguing both sides, but if we recognize what is ''most likely'' true, we may then proceed with a reasonable assumption, just to see where it leads. If it leads nowhere (i.e., a ''contradiction'') we immediately drop it and pick up the opposing argument to see where it might lead us. And so forth.

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'''NUMBER 4: [[Suez Canal]]'''

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::Around the 13th century BC, the Suez Canal was dug between the Nile River and the Red Sea.

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Why? Why would the ancient Egyptians dig a canal for ships to pass in the [[13th century BC]]? But wait ... there is more ... (posted at [[Silk Road]]''': Origins,''' bottom paragraph)

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::A maritime "Silk Route" opened up between Chinese-controlled Jiaozhi (centred in modern Vietnam, near Hanoi) probably by the first century CE. It extended all the way to Roman-controlled ports in Egypt and the Nabataean territories on the northeastern coast of the Red Sea. However, it is unclear whether this route circumnavigated the African continent (unlikely) or made passage through a temporarily maintained Suez Canal (more likely). The Hou Hanshu records that the first Roman envoy arrived in China by this maritime route in 166 CE.

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How long would it take to paddle (against the wind, against the currents, but sometimes ''with'' the wind) from Rome to Vietnam? ''Or do you think they had something more than just ''muscle-power'' on board? My muscles get sore just thinking about it.

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See also [[Bridge]]''': History,''' [[Cement]], and [[Origins of chess]] to think about. Some of this is also posted at [[Roman Empire]].

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You'd likely find [[Latin alphabet]]''': Evolution''' interesting as well.

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Do you believe Wikipedia is a reliable encyclopedia? Must we really provide you with more???

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:This is a bit off-topic for this talk page, but: one does not need to postulate ancient steam engines to explain the trade between Rome and China. Navigation and shipbuilding being what they were in that era, the trade necessarily went in stages: from China to Southeast Asia, from Southeast Asia to the eastern coast of India and Sri Lanka; from there to the west coast of India, whence it was traded, through the Red Sea ports, to Rome. —[[User:Mirv|Charles]][[User talk:Mirv| P.]][[Special:Emailuser/Mirv| (Mirv)]] 12:29, 8 Feb 2005 (UTC)

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Let me go through your points one at a time:

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First, it is quite obvious that the builders of the Great Pyramid were astute craftsmen and very likely methodical observers of the heavens. That they had science is not the issue here; my major nitpick with the above removals is that they are presented in a non-neutral fashion. They proceed from a form of argument and criticism, rather than from the neutral perspective of reporting on arguments and criticisms. Articles can present conflicting theories, but they must do so in an unbiased fashion, without showing preference for one theory or another. The amount of coverage each theory gets should be relatively proportional to the amount of acceptance they have (both scientific and metaphysical), but there's no hard rule on that either; the only hard rule is the [[Wikipedia:Neutral point of view|neutral point of view]].

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Second, I agree that the builders of the Pyramid most likely knew of Pi, or at least a very good approximation of it. I wrote much of the section about the Pyramid's expression of Pi, and you may note how, even though I personally think there is an obvious and accurate Pi expression in the Great Pyramid, I made every attempt to keep this point of view in terms of reporting on it, rather than arguing for it.

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Third, the references you have given here (at least the Britannica ones) strike me as very good examples of why Wikipedia is often better than Britannica. Not only is Wikipedia more easily available (along with the references used in writing the article, where applicable), it covers a broader range of conflicting theories than Britannica does. We can do better than Britannica: we need not state the most well-accepted theories as though they were universally accepted. But in order to do that, we need to stick to the neutral point of view.

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Fourth, I agree with Charles P. that it needn't be necessary to have steam engines to make such a journey feasible. Whether the builders of the Great Pyramid had steam power or not, this article shouldn't lead readers into believing that's the only logical conclusion. Present it neutrally, and I have no problem with this content. -- [[User:Wapcaplet|Wapcaplet]] 23:20, 8 Feb 2005 (UTC)

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::''The general formula for a frustum was evidently known to the Egyptians.... Speculate on how the Egyptians could have known the formula for a frustum, given that its derivation depends on the methods of modern calculus.''

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*[http://www.math.tamu.edu/~don.allen/ Allen, G. Donald], Professor, Director of Technology Assisted Instruction, Associate Head for Undergraduate Studies. Department of Mathematics, Texas A&M University, College Station, Texas, U.S. April 2001. [http://www.math.tamu.edu/~don.allen/history/egypt/node4.html ''The Moscow Papyrus''].

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If by "modern calculus" Mr. Donald is referring to calculus as we know it (via Newton and Leibniz), then modern calculus is by no means necessary for deriving a generalized formula for the volume of a pyramid. [http://www.mathpages.com/home/kmath343.htm Archmimedes did it] using the method of exhaustion, and [http://www.staff.hum.ku.dk/dbwagner/Pyramid/Pyramid.html Liu Hui] did it in the third century A.D. At any rate, I don't dispute that the Great Pyramid builders may have known a form of calculus, but I don't see how this reference (the speculative opinion of one professor) offers much by way of supporting the text that was removed from this article. -- [[User:Wapcaplet|Wapcaplet]] 02:28, 18 Feb 2005 (UTC)

Talk:Great Pyramid of Giza

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-"Additionally, it has been alleged (notably by the "sleeping prophet" Edgar Cayce?) that the dimensions and details of the great pyramid, properly interpreted, provide prophecies of events in modern times."
-No, Cayce said a lot of ... questionable things, but I think the "dimensions giving prophecy" schtick was somebody else's. I'll look and let you know. Some Italian guy .... not Schiaparelli. More later.
-- Here
-http://www.skeptics.com.au/journal/paramyth.htm
-Invented by John Taylor, elaborated by Charles Piazzi Smyth, Astronomer Royal for Scotland (my "Italian guy"  - don't know what his ethnicity was really.)
-----
-Yeah, I may be misremembering that, but I'm pretty sure he at least commented on it (but then he commented on just about every other bit of psychic nonsense of his time).  --LDC
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-I see Cayce "readings" on the Web that mention the idea, but it's difficult to pin down Cayce's language as to what he's really trying to say.
--- Here
-http://www.nhne.com/specialreports/srpyramid.html
-a "reading" about a secret hall of records of *ancient* events, not specifying whether this includes prophecies or not.
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-LOL - http://www.margaretmorrisbooks.com/xcerpt08.html
-- the following "shows that some of the claims associated with this idea are too strange to take seriously".
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-We should have something in the page about the astronomical alignments, also.
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-Kate Spence has a theory on astronomical alignments. Unfortunately her Nature article of 11 Nov 2000 seems unavailable, but a google search of "Kate Spence" reveals a cached page with the article; look for header "Feature of the week > Pyramid precision".
-:I have a copy of the paper. Spence figures several pyramid baselines were set in
-:How long it took to finish them is another question. Also, it's been several years; I don't know what the current thinking about Spence's work is.
-:--[[User:Wwoods|wwoods]] 00:29, 23 May 2004 (UTC)
-The statement that the pyramid has moved 4 kilometers South could also mean its original alignment has also shifted. Is there a reference concerning the 4 kilometer shift?
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-'''Date of completion:'''  I've just changed 2680 to 2570. 2680 is about 100 years too early, particularly in light of the dates given for [[Khufu (pharaoh)|Khufu]]'s reign in his article. 2570 would place completion in the final years of K's stint in the top spot.
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-So, what are the dimensions of the pyramid? The imperial and metric measurements don't exactly agree with each other (only accurate to 2 s.f.).
-Also, where does 52 degrees come from? If we take ''h'' as 146m and ''s'' as 235m, my calculations show that it is approximately 41 degrees:
-<math>\tan^{-1} \left( \frac{\frac{h}{\sin \left( 45^\circ \right) }}{s} \right) \approx 41.303^\circ</math>
--[[User:Zhen Lin|Zhen Lin]] 16:23, 14 Apr 2004 (UTC)
-:A cross-section of the pyramid containing the peak and parallel to opposite sides of the base will be a triangle of height 146.5&nbsp;m and base 230.5&nbsp;m. Therefore, the slope of the sides of the pyramid is
-:<math>\tan^{-1}\left({146.5\over230.5/2}\right)\approx51.81^\circ.</math>
-:&mdash;[[User:Bkell|Bkell]] 04:32, 13 Jun 2005 (UTC)
-== References? ==
-I'd be interested to see some references for the following statements in the article:
-# The chamber which is most normal in its situation is the subterranean chamber; but this is quite unfinished, hardly more than begun.
-# ...there is very credible testimony to a sarcophagus having existed in the queen's chamber, as well as in the king's chamber.
-# It was previously believed that slaves were used as labor, but that view is now rejected by almost all modern-day scholars.
-For (1), it's unclear to me what "normal" standard of reference is being used. Other pyramids? And by "unfinished", are we assuming that the chambers within the pyramid were intended for use as tombs? (I find it somewhat unlikely that anyone would go to all the trouble to build the Great Pyramid and then not bother "finishing" the inside.) For (2), what is the "very credible testimony"? And for (3), some more explanation about who, in particular, devised and supported the slave-labor theory, and maybe the names of a couple of the "almost all" scholars who have since rejected that theory. I'll see if I can't find some references for these myself, in the meantime... -- [[User:Wapcaplet|Wapcaplet]] 21:48, 22 May 2004 (UTC)
-:'''Unfinished Chamber'''
-:This unfinished subterranean chamber, an unfinished chamber within Khufu's Pyramid, lies 90 feet (30 meters) below the surface of the plateau, and is closed to the public. Standing alone inside this oxygen-deficient space is quite an experience; 2.3 million blocks of stone weighing some 6.5 million tons loom overhead. Workers down here chipped away at the limestone bedrock to build what is thought to be the original burial chamber for King Khufu. Egyptologists believe the chamber is 'unfinished' because Khufu suddenly decided he wanted his burial chamber to be higher in the pyramid, and ordered the workers to stop. Khafre's Pyramid follows a similar pattern, with an unfinished subterranean burial chamber.
-:http://www.pbs.org/wgbh/nova/pyramid/explore/khufuunflo.html
-:'''Queen's Chamber'''
-:Although it is called the 'Queen's Chamber,' Egyptologists believe this space was meant to be the final resting place for King Khufu, until he changed his mind yet again and opted for a burial chamber even higher. The roof of the chamber is raised at its center.
-:http://www.pbs.org/wgbh/nova/pyramid/explore/khufuqueenhi.html
-:--[[User:Wwoods|wwoods]] 00:29, 23 May 2004 (UTC)
-Those are good, though almost as vaguely worded as what we already have. I did find a fairly thorough source on construction, labor force, orientation, etc. [http://www.touregypt.net/featurestories/pyramids.htm here] (skip past the lame touristy introduction to the links at the bottom), including some great [http://www.touregypt.net/featurestories/pyramidlifts.htm illustrations] about how possible ramp configurations used to get blocks up the side. Lots of references to the specific people who came up with various theories. I think I'll build on those when I find some time.
-Also, I've been thinking about that claim to a [[pi]] ratio. It all boils down to the exact angle of the slope; if my math is correct, a slope of 51&deg;51'14.306" would yield pi accurate to six decimal places. Most of the measurements I've seen indicate that the slope is closer to 51&deg;50'40", giving pi accurate to 2 decimal places (3.142668...), closer to 22/7 than pi. I've seen varying estimates of the slope, though; less than 1 minute of error makes all the difference. -- [[User:Wapcaplet|Wapcaplet]] 04:41, 23 May 2004 (UTC)
-== New image addition ==
-The recently-added image [[:Image:Pyramids of Egypt.jpg]] does not appear to resemble anything now standing on the Giza plateau. Unless the illustration really is of the Giza pyramids, particularly the Great Pyramid (albeit a quite liberal interpretation), I don't think it belongs on the article. -- [[User:Wapcaplet|Wapcaplet]] 19:16, 24 Nov 2004 (UTC)
-* After looking around a bit, it appears that this image is by 16th-C. Dutch artist [[Martin van Heemskerck|Maerten van Heemskerck]]. [http://encarta.msn.com/media_461538596/engraving_of_Pyramids_of_Egypt.html] Judging by the resemblance, I'd say he must have done the engraving based on verbal description alone. I still don't think it belongs here. Maybe on [[Seven Wonders of the World]], since it needs an image. -- [[User:Wapcaplet|Wapcaplet]] 19:29, 24 Nov 2004 (UTC)
-:: I agree, and said as much on [[Image talk:Pyramids of Egypt.jpg|its talk page]]. If no one objects by the end of the week I'm going to change the image text or delete it entirely.  I don't care if I orphan it.  If it's near and dear to someone's heart you'd better come to its rescue. &mdash; [[User:Clarknova|Clarknova]] 03:25, 1 Dec 2004 (UTC)
-==Close-up picture==
-That's Khafre, not Khufu.
-* So it is. And someone also removed the "right" indicator in the caption to the other image showing all three. I've fixed to clarify (kept the image, though). -- [[User:Wapcaplet|Wapcaplet]] 19:32, 3 Feb 2005 (UTC)
-==NPOV==
-This article is beginning to need a neutrality overhaul. I [http://en.wikipedia.org/w/index.php?title=Great_Pyramid_of_Giza&diff=9935831&oldid=9918351 started], but there's much left to do. For instance:
-* "''As has been proven by papyrus documents, each side measured in Antiquity 440 Old Royal Cubits (230.5 m).''" -- Reference is needed. What papyrus documents?
-::''For the reference:'' &nbsp; Look to this [http://www.fig.net/pub/athens/papers/wshs2/WSHS2_1_Lelgemann.pdf document] ''(section 2.1)'' of the Director of the Berlin Geodesic Institute: He mentions in his article Mr. Petrie who found  this papyrus document in 1934.<br>
-:: -- [[User:Paul Martin|Paul Martin]] 22:42, 28 Feb 2005 (UTC)
-::P.S. ''The metrologist Livio C. Stecchini wrote:'' "It is agreed amount serious scholars that the side was calculated as 440 Egyptian royal cubits."
-* "''The grand gallery also contained some sort of mechanism for the release of a huge stone block which plugged the ascending passage.''" -- I don't doubt that this is true, but some evidence for and better description of such a mechanism would be useful.
-* "''The entire upper part of the pyramid was thus sealed after the burial of the king.''" -- Again, how do we know this? As far as I know, no evidence exists that a king was even buried here. We need references one way or another. There are other references throughout to "burial chamber of the king", "king's burial chamber", etc. which should probably be rendered as simply "King's chamber," given the dispute over whether a king was actually buried here.
-* An oddity about the "graffiti" on the relieving stones in the King's chamber: that it is "''the only evidence which proves that pharaoh Hor Medjedu Khnum Khufu had the Great Pyramid built.''" If this is the ''only'' evidence, then it's hardly proof of the pyramid's builder; this matter is under dispute, and maintaining neutrality requires that we try to avoid such unilateral statements.
-* In the section detailing various estimates of the labor force required, the section "''Nevertheless, given the subsequent absurd implications of these theories ... they fall terribly short of providing a satisfactory explanation''" is in serious need of rephrasing. Whether a theory is absurd or satisfactory is rather subjective; put the notion of absurdity in context, and make note of who finds the various theories absurd or satisfactory (or, better, simply note some of the theories, are those who dispute them, and let readers make their own judgments).
-* The article is arguing with itself. "''Second, if huge quantities of earth were dug and moved to support the ramps instead, geological indications would undoubtedly reveal this today. (Present day studies do yield such a revelation! But the ramp size uncovered is too small. See external links below.)''" This is bad. It gets even more ridiculous in the sentences that follow.
-* "''Some sort of ancient Steam engine is undeniably and absolutely required for a reasonable time period within which to carefully construct such a monument of this size.''" This is qualified in previous sentences, but it still comes across as being a statement of fact, especially with the excessive emphasis used.
-* Finally, the image at the very bottom showing "RJ or RL-shaped supports" needs some kind of reference. I couldn't find anything about these supports via Google.
-The total effect of the above is to make the article seem non-credible. Let's see if we can clean it up. -- [[User:Wapcaplet|Wapcaplet]] 20:48, 6 Feb 2005 (UTC)
-----
-OK, in a second crack at culling the POV, I've removed some things. First, this paragraph:
-<blockquote>Nevertheless, modern estimates for ancient Egyptian population size around the time that the pyramid was constructed fail at lending substantial credence for these assertions.  (See http://www.etext.org/Politics/World.Systems/papers/modelski/geocit.htm .)  And there are other serious technical questions posed as well, discussed as follows.</blockquote>
-The article referenced makes little mention of Giza, and none whatever regarding the population estimate being in conflict with various labor force size estimates for the Great Pyramid. I have also removed:
-<blockquote>Nevertheless, given the subsequent absurd implications of these theories -- ... in 2600 BC ... covering an area of seven city blocks and weighing six and a half million tons ... in less than thirty years, the workers had to raise over two million blocks to a height of forty stories at the rate of one block every three minutes ... [using] only the simplest technology (http://www.pbs.org/wgbh/nova/transcripts/1915mpyramid.html) -- they fall terribly short of providing a satisfactory explanation.</blockquote>
-Indeed, ''this article'' does not provide a very convincing explanation of how this may have been accomplished, and this is one area that could use some work. However, this part of the article is merely noting some of the estimates that have been made regarding the labor force needed. It's not our job (as authors of this article) to point out flaws in the reasoning of those who did the estimates. If you need to point out flaws, please find another publication that does it for you, and reference it.
-The next removal:
-<blockquote>Though this "ramp theory" is the popular perception today, it is not without some serious fundamental problems.  First, there remains considerable debate over exactly what kinds of ramps might have been used, because various ramp designs implicate technological advances that the ancient Egyptians clearly did not have.  (See [[Civil engineering]].)  Second, if huge quantities of earth were dug and moved to support the ramps instead, [[Geology|geological]] indications would undoubtedly reveal this today. (Present day studies ''do'' yield such a revelation! But the ramp size uncovered is too small. See external links below.)  Third, given even adequate resolutions to these first two problems, the most serious fundamental problem still remaining is that of ''time.''  Even if we were to multiply the given time period above (i.e., 30 years) many, many times over, we would still fail once again at reaching a workable conclusion.  Only by lengthening the given time period to ''several millennia (!)'' may we arrive at an adequate time frame with which to cut (''with [[chisel]]s?''), transport (''[[mile]]s!''), lift (''human muscle?''), maneuver (''with [[wood|board]]s and [[rope]]?'') and fit (''smoothing/reshaping some'') each of the over two million stone blocks!  ''Note that some of the stone blocks weigh several [[ton]]s!!''</blockquote>
-It was much easier to remove this paragraph than to edit out all the exclamation points (both literal and metaphorical). This was cut for the same reasons as above. Articles shouldn't make unsupported assertions (that is, assertions backed up only by patchwork arguments, rather than by references). Ditto for the following:
-<blockquote>Modern day [[Historical revisionism|Revisionists]] speculate that there could be only one logical conclusion to explain all the above.  (See also [[Origins of chess|origins of chess]] and [[Silk Road]]'':  '''Origins,''' bottom paragraph,'' for an adequate understanding.)  The only way possible that the ancient Egyptian laborers could have accomplished this monumental feat in anything resembling a reasonable amount of time is with [[chain]]s/[[cable]] and some sort of [[Crane (machine)|Ancient crane]].  The conclusion may run contrary to popular perception, but the facts point only in this direction.  Some sort of ancient [[Steam engine]] is ''undeniably'' and ''absolutely'' required for a reasonable time period within which to carefully construct such a monument of this size.  ''See external links and image below.''</blockquote>
-The end result is that this section of the article is more or less as it was at the beginning of November 2004. I don't deny that this section is in need of much work, but the above paragraphs do more harm than good, in my estimation. If anyone is interested in restoring these paragraphs, please back them up with references: facts, publications, and who, especially, has made these assertions. -- [[User:Wapcaplet|Wapcaplet]] 04:45, 7 Feb 2005 (UTC)
-== Rushing to Defend an Erroneous Deletion ==
-Dear Mr [[User:Wapcaplet|Wapcaplet]]:
-We understand your point of view.  History says one thing, but rational logic says another.  [[Historical revisionism]] always begins this way.
-History is repeating itself, because this same sort of affair happened in March of 2004 at [[Origins of chess]] when we first proposed an ancient Egyptian origin to the game.  Needless to say, the proposal was blasted off the web page and moved to "Talk."  Nevertheless, we sat quietly and watched as everyone pondered it over ... and what do you know?  Have you read [[Origins of chess]] lately?  There's even a photograph of the [[Sphinx]] and the [[Great Pyramid of Giza]] at the very top of that web page now!
-So, here we go again ....  :)
-The following discussion is rooted in web links that I've been able to find on the Internet.
-'''NUMBER 1:'''  To respond to your earnest request,
-::If anyone is interested in restoring these paragraphs, please back them up with references: facts, publications, and who, especially, has made these assertions,
-let's start by quoting ''... '''Wikipedia!!!''' ''
-::'''[[Scientific method]]:''' Our earliest records of ''anyone'' (much less a scientist) adhering to this strict process comes from ancient Egypt.
-You see.  The ancient Egyptians were using the scientific method ''millennia'' before [[Francis Bacon]] even knew how to write.  And see here: [[Bridge]]''': History''' and [[Cement]].  We could pile one astounding advance on top another.  Take a look at the pyramids:  Millions of stone blocks ... some weighing several tons.
-[[Ancient history]] proceeds in probabilities. The ancient Egyptians knew the scientific method ''millennia'' before anyone else did.  What are the implications?  Francis Bacon lived and died only a few hundred years ago.  [[Isaac Newton]], around the same time.  English history records only a short span of time (relatively speaking) between scientific processes and mathematical advancement.
-Here are some others you'd likely find interesting:
-::[[Demographics of Egypt]]:  Archeological findings show that primitive tribes lived along the Nile long before the dynastic history of the pharaohs began. By 6000 B.C., organized agriculture had appeared.
-::[[Figurine]]:  Read the bit on [[Morocco]].
-'''NUMBER 2:  [[Moscow and Rhind Mathematical Papyri]]'''
-::In summary, we cannot prove that the ancient Egyptians knew calculus. We can say however that the evidence suggests so.
-::In addition to these two historical texts, there is other evidence demonstrating an ancient Egyptian knowledge of basic mathematics and even [[surveying]] as early as [[3000 BC]].  [http://ag.arizona.edu/ABE/People/Faculty_Homepages/Cuellos_Homepage/Thoughts/ibe7.htm [1]]  See also [[Timeline of mathematics]].
-::Besides describing how to obtain an approximation of <math>\pi</math> accurate to within less than one per cent, it also describes one of the earliest attempts at [[squaring the circle]] and in the process provides persuasive evidence against the theory that the Egyptians deliberately built their [[pyramid]]s to enshrine the value of <math>\pi</math> in the proportions. Even though it would be a strong overstatement to suggest that the papyrus represents even rudimentary attempts at analytical geometry, Ahmes did make use of a kind of an analogue of the [[cotangent]]. Furthermore, quoting ''Mathpages.com,''
-::::... the 2/n table of the Rhind Papyrus, which dates from more than a thousand years before Pythagoras, seems to show an awareness of prime and composite numbers, a crude version of the 'Sieve of Eratosthenes,' a knowledge of the arithmetic, geometric, and harmonic means, and of the 'perfectness' of the number 6.  This all seems to suggest a greater number-theoretic sophistication than is generally credited to the ancient Egyptians. ([http://mathpages.com/home/rhind.htm ''The Rhind Papyrus 2/N Table''])
-'''NUMBER 3:  Population Size'''
-::Many varied estimates have been made regarding the labor force needed to construct the Great Pyramid. Herodotus, the Greek historian in the 5th century BC, estimated that construction may have required the labor of 100,000 slaves for 30 years. Polish architect Wieslaw Kozinski believed that it took as many as 25 men to transport a 1.5-ton stone block; based on this, he estimated the workforce to be 300,000 men on the construction site, with an additional 60,000 off-site.
-The key number here is 300,000, because it has been argued that the ancient Egyptians ''could have supplemented their work force'' with slaves.  Here are a couple references you'd likely be interested in:
-::[http://timelines.ws/0B3300_1300BC.HTML ''Timeline 3300 to 1300 BCE'']:  ''ca 2800BCE - Khufu commanded the building of the Great Pyramid. It took an estimated 100,000 people 30 years to construct.'' (WH, 1994, p.12)(K.I.-365D, p.122)(HT, 5/97, p.26)
-::[http://lexicorient.com/cgi-bin/eo-direct-frame.pl?http://i-cias.com/e.o/egypt_a.htm  ''Encyclopaedia of the Orient'']:  ''The main urban places of Egypt through the main part of the history of Ancient Egypt, were Memphis and Thebes.''
-To pause before continuing,
-*100,000 is too small a number.  Herodotus, who lived in the 5th century BC, didn't know what he was talking about.  Kozinski calculated a better number, but his number is too big, as evidenced by Professor Modelski's paper.
-*Even if you don't consider Memphis' proximity to the Great Pyramid of Giza significant, you must yield to its prominent status in ancient Egyptian history as ''capital'' and ''main urban place.''
-Nevertheless, as pointed out, population size is '''NOT''' ''the most serious fundamental problem.''  This is an important point, as said before [[Ancient history]] proceeds in probabilities.  We may spend an entire day arguing both sides, but if we recognize what is ''most likely'' true, we may then proceed with a reasonable assumption, just to see where it leads.  If it leads nowhere (i.e., a ''contradiction'') we immediately drop it and pick up the opposing argument to see where it might lead us.  And so forth.
-'''NUMBER 4:  [[Suez Canal]]'''
-::Around the 13th century BC, the Suez Canal was dug between the Nile River and the Red Sea.
-Why?  Why would the ancient Egyptians dig a canal for ships to pass in the [[13th century BC]]?  But wait ... there is more ... (posted at [[Silk Road]]''': Origins,''' bottom paragraph)
-::A maritime "Silk Route" opened up between Chinese-controlled Jiaozhi (centred in modern Vietnam, near Hanoi) probably by the first century CE. It extended all the way to Roman-controlled ports in Egypt and the Nabataean territories on the northeastern coast of the Red Sea. However, it is unclear whether this route circumnavigated the African continent (unlikely) or made passage through a temporarily maintained Suez Canal (more likely). The Hou Hanshu records that the first Roman envoy arrived in China by this maritime route in 166 CE.
-How long would it take to paddle (against the wind, against the currents, but sometimes ''with'' the wind) from Rome to Vietnam?  ''Or do you think they had something more than just ''muscle-power'' on board?  My muscles get sore just thinking about it.
-See also [[Bridge]]''': History,''' [[Cement]], and [[Origins of chess]] to think about.  Some of this is also posted at [[Roman Empire]].
-You'd likely find [[Latin alphabet]]''': Evolution''' interesting as well.
-Do you believe Wikipedia is a reliable encyclopedia?  Must we really provide you with more???
-:This is a bit off-topic for this talk page, but: one does not need to postulate ancient steam engines to explain the trade between Rome and China. Navigation and shipbuilding being what they were in that era, the trade necessarily went in stages: from China to Southeast Asia, from Southeast Asia to the eastern coast of India and Sri Lanka; from there to the west coast of India, whence it was traded, through the Red Sea ports, to Rome. &#8212;[[User:Mirv|Charles]][[User talk:Mirv|&nbsp;P.]][[Special:Emailuser/Mirv|&nbsp;<sup><small>(Mirv)</small></sup>]] 12:29, 8 Feb 2005 (UTC)
-----
-Let me go through your points one at a time:
-First, it is quite obvious that the builders of the Great Pyramid were astute craftsmen and very likely methodical observers of the heavens. That they had science is not the issue here; my major nitpick with the above removals is that they are presented in a non-neutral fashion. They proceed from a form of argument and criticism, rather than from the neutral perspective of reporting on arguments and criticisms. Articles can present conflicting theories, but they must do so in an unbiased fashion, without showing preference for one theory or another. The amount of coverage each theory gets should be relatively proportional to the amount of acceptance they have (both scientific and metaphysical), but there's no hard rule on that either; the only hard rule is the [[Wikipedia:Neutral point of view|neutral point of view]].
-Second, I agree that the builders of the Pyramid most likely knew of Pi, or at least a very good approximation of it. I wrote much of the section about the Pyramid's expression of Pi, and you may note how, even though I personally think there is an obvious and accurate Pi expression in the Great Pyramid, I made every attempt to keep this point of view in terms of reporting on it, rather than arguing for it.
-Third, the references you have given here (at least the Britannica ones) strike me as very good examples of why Wikipedia is often better than Britannica. Not only is Wikipedia more easily available (along with the references used in writing the article, where applicable), it covers a broader range of conflicting theories than Britannica does. We can do better than Britannica: we need not state the most well-accepted theories as though they were universally accepted. But in order to do that, we need to stick to the neutral point of view.
-Fourth, I agree with Charles P. that it needn't be necessary to have steam engines to make such a journey feasible. Whether the builders of the Great Pyramid had steam power or not, this article shouldn't lead readers into believing that's the only logical conclusion. Present it neutrally, and I have no problem with this content. -- [[User:Wapcaplet|Wapcaplet]] 23:20, 8 Feb 2005 (UTC)
-----
-::''The general formula for a frustum was evidently known to the Egyptians.... Speculate on how the Egyptians could have known the formula for a frustum, given that its derivation depends on the methods of modern calculus.''
-*[http://www.math.tamu.edu/~don.allen/ Allen, G. Donald], Professor, Director of Technology Assisted Instruction, Associate Head for Undergraduate Studies. Department of Mathematics, Texas A&M University, College Station, Texas, U.S.  April 2001. [http://www.math.tamu.edu/~don.allen/history/egypt/node4.html ''The Moscow Papyrus''].
-If by "modern calculus" Mr. Donald is referring to calculus as we know it (via Newton and Leibniz), then modern calculus is by no means necessary for deriving a generalized formula for the volume of a pyramid. [http://www.mathpages.com/home/kmath343.htm Archmimedes did it] using the method of exhaustion, and [http://www.staff.hum.ku.dk/dbwagner/Pyramid/Pyramid.html Liu Hui] did it in the third century A.D. At any rate, I don't dispute that the Great Pyramid builders may have known a form of calculus, but I don't see how this reference (the speculative opinion of one professor) offers much by way of supporting the text that was removed from this article. -- [[User:Wapcaplet|Wapcaplet]] 02:28, 18 Feb 2005 (UTC)